Problem: Solve for $x$. $8^7=8^3\cdot8^x$ $x=$
When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${8^7}={8^3}\cdot8^x}$. $\begin{aligned} &={\underbrace{8\cdot8\cdot8}_\text{3 times}}\cdot\underbrace{ }_{x\text{ times}}} \\\\\\ &={\underbrace{8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8}_\text{7 times}} \\\\ \end{aligned}$ $x=4$